I recently purchased a copy stand to digitize my company's watercolor library. I am using two RPS CL150 arm-light attachments; however, I keep getting two large spotlights on the paintings where the lights isn't diffusing evenly. I have tried pulling the lights farther out, but it drastically darkens the photograph and I am still getting poor results when I place a white cloth over the bulbs. If anyone has any insight into what I am doing wrong or if there is a better alternative—bulbs, lighting equipment, etc.—it would be extremely helpful.
Basically there are two things you can do to eliminate the two spot lights, you will probably want to do both - and I think both are not possible with the arm light attachments (so you may need to get other lights)
Change the angle of the lights
The "spotlight effect" you see is actually the reflection of the light on the painting, if the light are at a close angle to the camera the reflection will be visible in the photo - but if the light is at a very different angle then the camera then most of the reflection will be projected "sideways" and not into the lens
Note that putting the light at a very shallow angle will really exaggerate the texture of the paint and paper - so don't over do it.
Diffuse/soften the light
To diffuse the light you really need to make the light source bigger, putting a white cloth on the light helps a little bit, putting a big cloth a small distance in front of the light will be much better.
That is why photographers put umbrellas in front of flashes - it spreads the light so the the entire umbrella becomes a huge light source instead of a tiny flash bulb.
Now both of those will lower the usable power of your lights, by projecting the reflections away from the camera you are also throwing away a lot of light and spreading the light over a large area will significantly reduce the intensity of the light.
You either have to compensate with the camera settings or get more powerful lights (or possibly both), flashes are popular because they give out an enormous amount of light (for a very very short amount of time) giving you the ability to waste most of the light but to get better results.
Also, as R Hall said, color management can be a major issue but you can overcome it by using only the same controlled lights (close all windows and dim the room lights) by taking a picture of a gray card in the exact setup you use at the beginning of every session and by shooting in raw - then later you can use any raw processing software you want to calculate the light balance based on the gray card and apply to the rest of the images - and use only good full spectrum lights - no cheap fluorescent and led lights (modern higher end fluorescent aren't bad, indecent bulbs or good photography lights are best)
More than likely your problem is that the lights are too close. Watercolors are generally bigger than 8x10 for example. A copy stand generally has the lights too close for works bigger than a book.
One bad solution is to put put a scrim or light modifier in between the light and the watercolors. It may eliminate the hot spot but create an new problems with low contrast and a reflection, although faint.
If your problem is one of distance, then polarizers won't really help. Polarizers often help, and have used them myself, but hotspots could be due to reflection or could be due to proximity. I find if I am shooting paintings, even watercolors, I like to use strobes and have them at least 6 feet away from the painting. Also if the painting or watercolor or poster is really flat, 30 degrees is a better angle for even distribution of lights.
I use two lights. I also like to use a strip soft box for more even lighting. Some photographers even use 4 lights one on each corner.
One tip, aim your lights at the opposite side of the watercolor.
There is no color management problem with strobes but be sure your strobes have UV filters over the flash tubes, to avoid harming the watercolor's pigments.
You can use even incandescent shop lights to light this work. What you need is enough light to do the job. This method works but it requires ventilation since the room gets warm. The real question with watercolor paintings is color rendering and color management. Tungsten lights have a high CRI so they will do the job.
The color management issue will be something to overcome though with watercolor pigments unless your company doesn't care much how their artwork is recorded.
You can try to use polarizing filters on your lights and another polarizing filter on your camera, rotated 90 degrees. I'll quote my own answer from a different question at this site.
There is another alternative: Use two polarizing filters, one on the lens and one on the flash, and rotate one of them by 90 degrees. The directly reflected light is polarized, and the flash reflection should be nearly cancelled out, where as your target produces a diffuse, non polarized reflection of the flash-light, which passes the filter on the lens. It's not perfect, but it should improve the results.